Use Multiple Image Editors in Compositor
You’re doing everything right.
This is just the way Blender works.

Here’s how you can make it work:
1) In one image editor choose Render Result from the top-down menu. This will show output from the Compositor Node.
2) In the other one choose Viewer Node to see output from selected Viewer Node.

As you noticed, Viewer Node only shows the last selected one. It’s a limitation of Blender.
However, you can use Split Viewer Node node to get side-by-side comparison.

How to make it work


Note:
Blender Compositor has some slight limitations, but hey, it’s free :).